1,045 research outputs found
Means on scattered compacta
We prove that a separable Hausdorff topological space containing a
cocountable subset homeomorphic to admits no separately
continuous mean operation and no diagonally continuous -mean for .Comment: 6 page
A scattering of orders
A linear ordering is scattered if it does not contain a copy of the rationals. Hausdorff characterised the class of scattered linear orderings as the least family of linear orderings that includes the class of well-orderings and reversed well-orderings, and is closed under lexicographic sums with index set in . More generally, we say that a partial ordering is -scattered if it does not contain a copy of any -dense linear ordering. We prove analogues of Hausdorff's result for -scattered linear orderings, and for -scattered partial orderings satisfying the finite antichain condition. We also study the -scattered partial orderings, where is the saturated linear ordering of cardinality , and a partial ordering is -scattered when it embeds no copy of . We classify the -scattered partial orderings with the finite antichain condition relative to the -scattered linear orderings. We show that in general the property of being a -scattered linear ordering is not absolute, and argue that this makes a classification theorem for such orderings hard to achieve without extra set-theoretic assumptions
Electromagnetic Hadronic Form-Factors
We present a calculation of the nucleon electromagnetic form-factors as well
as the pion and rho to pion transition form-factors in a hybrid calculation
with domain wall valence quarks and improved staggered (Asqtad) sea quarks.Comment: 3 pages, 5 figures, Lattice2004(spectrum
Ab initio derivation of multi-orbital extended Hubbard model for molecular crystals
From configuration interaction (CI) ab initio calculations, we derive an
effective two-orbital extended Hubbard model based on the gerade (g) and
ungerade (u) molecular orbitals (MOs) of the charge-transfer molecular
conductor (TTM-TTP)I_3 and the single-component molecular conductor
[Au(tmdt)_2]. First, by focusing on the isolated molecule, we determine the
parameters for the model Hamiltonian so as to reproduce the CI Hamiltonian
matrix. Next, we extend the analysis to two neighboring molecule pairs in the
crystal and we perform similar calculations to evaluate the inter-molecular
interactions. From the resulting tight-binding parameters, we analyze the band
structure to confirm that two bands overlap and mix in together, supporting the
multi-band feature. Furthermore, using a fragment decomposition, we derive the
effective model based on the fragment MOs and show that the staking TTM-TTP
molecules can be described by the zig-zag two-leg ladder with the
inter-molecular transfer integral being larger than the intra-fragment transfer
integral within the molecule. The inter-site interactions between the fragments
follow a Coulomb law, supporting the fragment decomposition strategy.Comment: 16 pages, 8 figures, published versio
A classification of CO spaces which are continuous images of compact ordered spaces
AbstractA topological space X is called a CO space, if every closed subset of X is homeomorphic to some clopen subset of X. Every ordinal with its order topology is a CO space. This work gives a complete classification of CO spaces which are continuous images of compact ordered spaces
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